Chapter 2.5, Problem 67MP

67. Using a graphing utility, graph $f\left(x\right)\text{ = }{x}^3\text{ - 9}x$ for $-4\le x\le \text{ 4}$.

(a) Find the $\text{x-intercepts}$ of the graph of $f$.

(b) Approximate any local maxima and local minima.

(c) Determine where $f$ is increasing and where it is decreasing.

(d) Without using a graphing utility, repeat parts (b)-(d) for $y\text{ = }f\left(x\text{ + 2}\right)$.

(e) Without using a graphing utility, repeat parts (b)-(d) for $y\text{ = 2}f\left(x\right)$.

(f) Without using a graphing utility, repeat parts (b)-(d) for $y\text{ = }f\left(-x\right)$.